- #1
jimmycricket
- 116
- 2
Homework Statement
Is [tex]f(x)=x^2+1[/tex] irreducible in [tex]\mathbb{F}_2[x][/tex]
If not then factorise the polynomial.
The Attempt at a Solution
[tex]\mathbb{F}_2[x]=\{0,1\}[/tex]
[tex]f(0)=1[/tex]
[tex]f(1)=1+1=0[/tex]
Hence the polynomial is not irreducible